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Published December 2003 | public
Book Section - Chapter

Barrier Certificates for Nonlinear Model Validation

Abstract

New methods for model validation of continuous-time nonlinear systems with uncertain parameters are presented in this paper. The methods employ functions of state-parameter-time, termed here as barrier certificates, whose existence proves that a model and a feasible parameter set are inconsistent with some time-domain experimental data. A very large class of models, including differential-algebraic models, models with memoryless/dynamic uncertainties, and hybrid models, can be treated within this framework. Construction of barrier certificates can be performed by convex optimization, utilizing the sum of squares decomposition of multivariate polynomials.

Additional Information

© 2003 IEEE. Date of Current Version: 15 March 2004. The author would like to thank Prof. John Doyle for suggesting the author to work on this topic and providing stimulating discussions. This work was supported by AFOSR "Unified Theory for Complex Biological and Engineering Networks", NIH/NIGMS Alliance for Cellular Signaling, DARPA "Enlightened Multiscale Simulation of Biochemical Networks", the Kitano ERATO Systems Biology Project, and URI "Protecting Infrastructures from Themselves."

Additional details

Created:
August 19, 2023
Modified:
October 24, 2023